You are correct, #1 is the only one that is in a passive voice.
As it's currently written, sentence 2 isn't quite grammatically correct. "I had not directly involved X with/in...," where X is the direct object, would be the grammatically correct form in active voice. In active voice, you become the doer, the one actively getting involved, and the object of the sentence is the receiver, with which you are getting involved.
This sentence can become passive if you change it to read "I had not been directly involved..." This makes you the receiver and the other entity as the doer, actively instigating and/or controlling your involvement.
This can completely change the meaning of the sentence depending on the context and what is being described. "I had not directly involved myself in the robbery" vs "I had not been directly involved with the robbery" imply different degrees of culpability.
Sentence 3, on the other hand, cannot be made into a passive statement simply by adding a verb. You also have to change the intransitive verb to a direct object. "I did not become directly involved with [it]," and, "I did not directly involve [them]," are both still active whereas, "I did not have direct involvement with [it]," is passive. Unlike #2, however, this has very little impact on the meaning of the sentence.
Breaking those sentence structures down, we can see that the only difference is in whether it employs an intransitive verb or a direct object. The effect of this being that 3a is in past perfect tense while 3b and 3c are both in past simple tense.
N V Adv V Adv Vi
3a I | did not | become | directly involved...
N V Adv V Adj DO
3b I | did not | have | direct involvement...
N V Adv Adv V DO
3c I | did not | directly involve | [them].